Bühlmann and Bühlmann–Straub Credibility Models with an Alternative Dependence Structure

Abstract

The traditional approach to the Bьhlmann and Bьhlmann–Straub models is based on a special type of dependence — known as the conditional independence. Although there have been some attempts to generalise these models, it is still difficult to understand what general conditions should be met for existence of solutions in the traditional form of the credibility estimator. Different forms of past experience that influence the predictor are discussed. Two different sets of assumptions regarding the alternative dependence structure and the type of estimator are discussed in this paper. For both approaches, the Bьhlmann and Bьhlmann–Straub models are specific cases.

Keywords:

quadratic loss function, variance–covariance matrix, uniform dependence, mechanism for the influence of past experience (data) on the predictor, best linear Bayes estimator